What is the asymptotes of 16y^2-25x^2=400 ?

The asymptotes of 16y^2-25x^2=400 is y=(5x)/4 ,\quad y=-(5x)/4

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asymptotes of 16y^2-25x^2=400

asymptotes

16 y^{2} - 25 x^{2} = 400

y = \frac{5 x}{4}, y = - \frac{5 x}{4}

Solution steps

y = \pm \frac{a}{b} (x - h) + k

Calculate Hyperbola properties

16 y^{2} - 25 x^{2} = 400 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 5, b = 4

y = \frac{5}{4} (x - 0) + 0, y = - \frac{5}{4} (x - 0) + 0

Refine

y = \frac{5 x}{4}, y = - \frac{5 x}{4}

x^{2} - y^{2} = 100

5 y^{2} - 16 x^{2} + 400 = 0

- 25 x^{2} + y^{2} = 25

5 x^{2} - 6 y^{2} - 20 x + 12 y - 16 = 0

\frac{y ^{2}}{1 2 ^{2}} - \frac{x ^{2}}{6 ^{2}} = 1

What is the asymptotes of 16y^2-25x^2=400 ?
The asymptotes of 16y^2-25x^2=400 is y=(5x)/4 ,\quad y=-(5x)/4